Efficient random sampling of binary and unary-binary trees via holonomic equations

Axel Bacher; Olivier Bodini; Alice Jacquot

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arXiv · 1401.1140

Efficient random sampling of binary and unary-binary trees via holonomic equations

Axel Bacher·Olivier Bodini·Alice Jacquot

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Abstract

We present a new uniform random sampler for binary trees with $n$ internal nodes consuming $2n + \Theta(\log(n)^2)$ random bits on average. This makes it quasi-optimal and out-performs the classical Remy algorithm. We also present a sampler for unary-binary trees with $n$ nodes taking $\Theta(n)$ random bits on average. Both are the first linear-time algorithms to be optimal up to a constant.

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Axel Bacher, Olivier Bodini, Alice Jacquot. 2014-01-06. Efficient random sampling of binary and unary-binary trees via holonomic equations. https://arxiv.org/abs/1401.1140

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